Playing this way with a partner really lessens your chance of experiencing complications and makes more play options available for the simple reason that you will have someone to help you if you pass out. Aside from that, if you have some form of injury occur you will have someone to help you get assistance. The main downside to play with a partner is that you have to spend a lot of time finding the person you will literally trust your life with and if something goes horribly wrong you may end up convicted of a crime or having your lover convicted of a crime. The physiological things mentioned in another section will all still be present so even if you play very "safe" you could end up drawing the short straw and taking the consequences. Out of 25 million people in the US, it is estimated that 250 will die of erotic asphyxiation in a year. Of those 250 almost all of them will be auto-erotic asphyxiation (solo play). Therefore, statistically your chances of partner play going wrong are pretty darn low if you pay attention to avoiding the risks you can control. With that in mind...let's talk about how things could be done and how to lower the risks.
This form of play requires a lot of caution. If you are somehow compressing the trachea it is important to do so by slowly applying pressure and making sure not to apply pressure to the larynx. One method is to take a curved finger and place it at the part of the throat where it meets the chin and pushing up and back slowly. Another method is to apply pressure below the larynx (sometimes with a scarf). A lot of injuries can occur to the trachea this way if you press too hard. If you are going to use a ligature or noose it is safer if you use one that doesn't constrict. If it does, make sure it is wide and padded. If it is too narrow it will cut or twist the skin causing bruising and damage to things such as blood vessels, nerves, the cervical spine, and the windpipe. It may also be a good idea to use a dry lubricant such as baby powder and a soft type of rope or ligature. If you are hanging someone it is important never to drop them into place. That could break their spine. I think a really nice form of rigging for hanging is when a person is raised into place with their feet still on the ground. If you decide to try airwalking there is a significant possibility of damage to the spine.